104 research outputs found
Deciding synchronous Kleene algebra with derivatives
Synchronous Kleene algebra (SKA) is a decidable framework that combines Kleene algebra (KA) with a synchrony model of concurrency. Elements of SKA can be seen as processes taking place within a fixed discrete time frame and that, at each time step, may execute one or more basic actions or then come to a halt. The synchronous Kleene algebra with tests (SKAT) combines SKA with a Boolean algebra. Both algebras were introduced by Prisacariu, who proved the decidability of the equational theory, through a Kleene theorem based on the classical Thompson -NFA construction. Using the notion of partial derivatives, we present a new decision procedure for equivalence between SKA terms. The results are extended for SKAT considering automata with transitions labeled by Boolean expressions instead of atoms. This work continous previous research done for KA and KAT, where derivative based methods were used in feasible algorithms for testing terms equivalence. (c) Springer International Publishing Switzerland 2015
Completeness and Incompleteness of Synchronous Kleene Algebra
Synchronous Kleene algebra (SKA), an extension of Kleene algebra (KA), was
proposed by Prisacariu as a tool for reasoning about programs that may execute
synchronously, i.e., in lock-step. We provide a countermodel witnessing that
the axioms of SKA are incomplete w.r.t. its language semantics, by exploiting a
lack of interaction between the synchronous product operator and the Kleene
star. We then propose an alternative set of axioms for SKA, based on Salomaa's
axiomatisation of regular languages, and show that these provide a sound and
complete characterisation w.r.t. the original language semantics.Comment: Accepted at MPC 201
Decision Procedure for Synchronous Kleene Algebra
Kleene Algebra (KA) is an algebraic system that has many applications both in mathematics and
computer science. It was named after Stephen Cole Kleene who extensively studied regular
expressions and finite automata [Kle56].
Moreover it is often used to reason about programs, as it can represent sequential composition,
choice and finite iteration. Furthermore, the need to reason about actions which can be executed
concurrently, spawned SKA. SKA is an extension of KA introduced by Cristian Prisacariu
in [Pri10] that adopts a notion of concurrent actions.
Laguange equivalence is an imperishable problem in computer science. In this thesis we present
the reader with a detailed explanation of a decision procedure for SKA terms and an OCaml
implementation of said procedure as well.A Kleene Algebra (KA) é um sistema algébrico que tem bastantes aplicações quer no campo da
matemática como também da informática.
Foi batizada com o nome do seu inventor Stephen Cole Kleene, que ao longo da sua carreira fez
um estudo intensivo sobre expressões regulares e autómatos finitos [Kle56].
Quando há necessidade de raciocinar equacionalmente sobre programas, recorre-se frequentemente
à Kleene Algebra, visto que esta consegue exprimir noções de escolha, composição sequencial
e até a noção de iteração. A necessidade de raciocinar equacionalmente sobre ações
que podem ser executadas de forma concorrente levou ao aparecimento da Algebra de Kleene
Síncrona ou Synchronous Kleene Algebra (SKA). Esta última foi introduzida por Cristian Prisacariu
em 2010 no seu artigo [Pri10] como uma extensão à Kleene Algebra mas que contém uma noção
de ação concorrente.
A equivalência de linguagens é um problema perene em ciências da computação. Nesta dissertação
iremos apresentar ao leitor uma explicação detalhada de um processo de decisão para
termos de Synchronous Kleene Algebra (SKA) bem como a sua implementação utilizando a linguagem
de programação OCaml
Brzozowski goes concurrent - A kleene theorem for pomset languages
Concurrent Kleene Algebra (CKA) is a mathematical formalism to study programs that exhibit concurrent behaviour. As with previous extensions of Kleene Algebra, characterizing the free model is crucial in order to develop the foundations of the theory and potential applications. For CKA, this has been an open question for a few years and this paper makes an important step towards an answer. We present a new automaton model and a Kleene-like theorem that relates a relaxed version of CKA to series-parallel pomset languages, which are a natural candidate for the free model. There are two substantial differences with previous work: from expressions to automata, we use Brzozowski derivatives, which enable a direct construction of the automaton; from automata to expressions, we provide a syntactic characterization of the automata that denote valid CKA behaviours
Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages
Concurrent Kleene Algebra (CKA) is a mathematical formalism to study programs that exhibit concurrent behaviour. As with previous extensions of Kleene Algebra, characterizing the free model is crucial in order to develop the foundations of the theory and potential applications. For CKA, this has been an open question for a few years and this paper makes an important step towards an answer. We present a new automaton model and a Kleene-like theorem that relates a relaxed version of CKA to series-parallel pomset languages, which are a natural candidate for the free model. There are two substantial differences with previous work: from expressions to automata, we use Brzozowski derivatives, which enable a direct construction of the automaton; from automata to expressions, we provide a syntactic characterization of the automata that denote valid CKA behaviours
On Series-Parallel Pomset Languages: Rationality, Context-Freeness and Automata
Concurrent Kleene Algebra (CKA) is a formalism to study concurrent programs.
Like previous Kleene Algebra extensions, developing a correspondence between
denotational and operational perspectives is important, for both foundations
and applications. This paper takes an important step towards such a
correspondence, by precisely relating bi-Kleene Algebra (BKA), a fragment of
CKA, to a novel type of automata, pomset automata (PAs). We show that PAs can
implement the BKA semantics of series-parallel rational expressions, and that a
class of PAs can be translated back to these expressions. We also characterise
the behavior of general PAs in terms of context-free pomset grammars;
consequently, universality, equivalence and series-parallel rationality of
general PAs are undecidable.Comment: Accepted manuscrip
Axiomatizing Prefix Iteration with Silent Steps
Prefix iteration is a variation on the original binary version of the Kleene star operation P*Q, obtained by restricting the first argument to be an atomic action. The interaction of prefix iteration with silent steps is studied in the setting of Milner's basic CCS. Complete equational axiomatizations are given for four notions of behavioural congruence over basic CCS with prefix iteration, viz. branching congruence, eta-congruence, delay congruence and weak congruence. The completeness proofs for eta-, delay, and weak congruence are obtained by reduction to the completeness theorem for branching congruence. It is also argued that the use of the completeness result for branching congruence in obtaining the completeness result for weak congruence leads to a considerable simplification with respect to the only direct proof presented in the literature. The preliminaries and the completeness proofs focus on open terms, i.e. terms that may contain process variables. As a by-product, the omega-completeness of the axiomatizations is obtained as well as their completeness for closed terms. AMS Subject Classification (1991): 68Q10, 68Q40, 68Q55.CR Subject Classification (1991): D.3.1, F.1.2, F.3.2.Keywords and Phrases: Concurrency, process algebra, basic CCS, prefix iteration, branching bisimulation, eta-bisimulation, delay bisimulation, weak bisimulation, equational logic, complete axiomatizations
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.
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